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Solve the linear Diophantine equation 11x - 13y = 1 using Euclid's algorithm.

\(\begin{array}{|rcll|} \hline 11x-13y=1 \\ \mathbf{11x+(-13)y=1} \\ \text{Euclid's Algorithm} &&&\text{remainder}\\ \hline -13 &=& -1\times11-2 & -2 = -13+11 \\ 11 &=& -5\times(-2)+1 & 1 =11+5\times(-2) \\ -2 &=& -2\times 1+0 \qquad \text{stop} \\ \hline \end{array} \)

\(\begin{array}{|rcll|} \hline \text{backwards substitution} \\ \hline 1 &=& 11+5\times(-2) \quad & | \quad -2=-13+11 \\ 1 &=& 11+5\times(-13+11) \\ 1 &=& 11+5\times(-13) +5\times+11 \\ 1 &=& 6\times 11+5\times(-13) \\ \hline x=6 && y=5 \\ &\text{check}& \\ 11\times 6 +5\times(-13) &=& 1\\ 66-65 &=& 1 \ \checkmark \\ \hline \end{array} \)

welllll     sqrt29 is not an integer    so   f (sqrt29)   =   |_sqrt29_| +5  = 10

6 p x 20 h  / 15r = 8 p-h / r

8 p-h / r   x   1 r / 1 p  = 8 hrs

Similar to just posted distance question

Use distance formula

(2a-4)^2   + (a-4 - -1)^2 =  (2 sqrt10)^2

4a^2 -16a + 16      +   a^2 -6a+9    = 40

5a^2 -22a -15 = 0    Use quadratic formula to find a =    5   or   -0.6    (if I made no mistakes!)

You are welcome.....I hope you understand the solution method ! 

3x   + 2 (25-x)  = 70      solve for 'x' the three point shots....then #2-pointers = 25-x

Thank you! 

Why is it +1 Instead of -1?

\((n-k+1)!\)

Use distance formula

(2- -1)^2  + (n-1)^2 = 5^2

9            + n^2 -2n+1 = 25

n^2 -2n -15 = 0      

(n-5)(n+3) = 0                 n = 5   or  -3

But I still don't understand how N choose K-1 = \(n!/(k-1)!(n-k+1)!\)

Thanks for the information!

Probability of driving to work alone        =  0.77

Probability of not driving to work alone  =  0.23

Total number of workers                         =  8

Probability that none drive to work alone:        ₈C₀·(0.77)⁰·(0.23)⁸  =  

Probability that exactly 5 drive to work alone:  ₈C₅·(0.77)⁵·(0.23)³  =

Probability that at most 4 drive to work alone:  [this would be either 4 or 3 or 2 or 1 or none of them]

 _{=   8}C₄·(0.77)⁴·(0.23)⁴  +  ₈C₃·(0.77)³·(0.23)⁵  +  ₈C₂·(0.77)²·(0.23)⁶  +  ₈C₁·(0.77)¹·(0.23)⁷  +  ₈C₀·(0.77)⁰·(0.23)⁸   =    

Web2 calculator will do this for you too  (use homepage version)

enter  .0072356

hit ' = '  

      look at area above calculator for another format

Area of WHOLE circle =  pi 8^2  = 64 pi

Angle of shaded area = 360-105 = 255 degrees

Shaded area is fraction of total area   255/360

255/360   *    64 pi = .......  in^2

Arc(CB)  =  90^o.

Arc(CBH)  =  90^o + 57^o  = 147^o.

Perimeter of circle  =  2·pi·r  =  2·pi·60  =  120·pi cm.

Portion of the circle:  arc(CBH)  =  147^o / 360^o.

Length of the arc =  (147/360)·120·pi cm

You'll need to get the decimal answer ...

First, 90= 2 * 3^2 * 5. We know that m must be multiple of 2,3 and 5. So LCM(2,3,5) = 30. So, it is 5. 

You are right!  In fact, if you look at my f(x)+f((x-1)/x) it doesn't equal g(x), there is multiplier of 5 that shouldn't be there!!

They ALREADY ARE in " standard form" ! However, you can convert them to "Scientific Notation" as follows:

0.0073256 = 7.3256  x  10^ - 3

0.05 =5.0 x 10^-2

0.5   =5 x 10^-1

1200256500 =1.2002565  x  10^9

alan, according to my calculations i believe the only possible answer is fx=5x-3!!!

1,10,19,... +9 each time

\(T_n=dn+c\) where d is a common difference (9) and c is the first term - d

\(T_n=9n-8\)

Thus the 21th term is 

\(T_{21}=9(21)-8=181\)

Deleted.  See below

(Clearly f(x) = (2 + 3x)/x is incorrect.)

A = 0.5*3*7*sin43°

A = 7.16

The arc length of an arc subtended by an angle measuring  11π/18 radians is 78.6 inches. What is the radius of the arc?

1 - (- 4) = 5

5² = 25

- 75 : 25 = - 3

a = - 3

Thanks Heureka